Optical amplifiers are emerging as practical components for use in various lightwave communication systems. Such optical amplifiers can enhance the performance of lightwave communication systems by boosting signal levels to overcome noise. However, generally, the gain of such amplifiers, and specifically the gain of preferred semiconductor optical amplifiers, is inherently nonlinear. Such nonlinearity can cause adverse, and potentially harmful, effects such as gain saturation, inter-modulation distortion (IMD) in frequency-division-multiplexed (FDM) systems employing closely spaced carriers (see, T. E. Darcie et al, Electron. Lett., 1987, Vol. 23, pp. 1392-1394; R. M. Jopson et al, Electron. Lett., 1987, Vol. 23, pp. 1394-1395; G. Grosskopf et al, Electron. Lett., 1988, Vol. 24, pp. 31-32; and T. E. Darcie et al, Electron. Lett., 1988, Vol. 24, pp. 638-640), crosstalk in wavelength-division-multiplexed (WDM) systems employing widely spaced on-off-keyed (OOK) or amplitude shift keyed (AMK) carriers (see, G. P. Agrawal et al, Electron. Lett., Vol. 23, pp. 1175-1177; and M. G. Oberg et al, IBEE J. Quantum Electron., 1988, Vol. QE-24, pp. 52-59, and pulse distortion in multi-Gb/s intensity-modulation systems, even those employing a single carrier.
Each of the above-mentioned nonlinear effects results from the coupling between the excited state density, and, hence, the optical gain, and the optical intensity within the amplifier. Gain saturation reduces the total output power of the amplifier for large input powers. Inter-modulation distortion (IMD) results from modulation of the gain by beating between closely spaced optical signals, and limits the maximum useable output power, or the minimum channel separation, in multi-channel frequency division multiplexed systems. Regardless of the channel separation, intensity modulation in one channel leads to modulation of the gain available for other channels. The resultant saturation induced crosstalk (SIC) impairs all multi-channel amplifier applications that use amplitude shift keying (ASK).
Some of these effects have been investigated theoretically (see, T. E. Darcie et al, Electron. Lett., 1987, Vol. 23, pp. 1392-1394; T. E. Darcie et al, Electron. Lett., 1988, Vol. 24, pp. 638-640; and G. P. Agrawal et al, Electron. Lett., 1987, Vol. 23, pp. 1175-1177) through the solution of a pair of coupled partial differential equations--the wave equation and the rate equation (see, G. P. Agrawal, Opt. Lett., 1987, Vol. 12, pp. 160-262; and G. P. Agrawal et al, Long-wavelength Semiconductor Lasers, Van Nostrand Reinhold, New York, 1986, Chapter 2). However, this technique is somewhat complex and is generally not suitable for analysis involving arbitrary input signals, particularly those having multi-Gb/s carriers.
These nonlinear effects can be made negligible by reducing the amplifier input power to a sufficiently low value. However, this can defeat the object of using such amplifiers. It is well known that by using constant-envelope modulation the inter-modulation distortion (IMD) in frequency division multiplexed (FDM) systems can be made acceptable by increasing the intercarrier separation to more than a few GHz. However, this may lead to an unacceptably inefficient use of the spectrum in multi-channel applications.